Applications of Mathematical Induction, Class 11 Mathematics NCERT Solutions

1. There will be total 15  MCQ in this test.
2. Please keep a pen and paper ready for rough work but keep your books away.
3. The test will consist of only objective type multiple choice questions requiring students to mouse-click their correct choice of the options against the related question number.
4. No negative marking for incorrect choice.
5. Please click on “Finish the Test” when you want to exit.
6. All the best – Happy Studying.

1. For each n ∈ N, 7²ⁿ + 16n - 1 is divisible by :

34

54

66

64

Question 1 of 15

2. If then A¹⁰ equals

A.   B.   C.   D.  

A

B

C

D

Question 2 of 15

3. 2.4^{2n + 1} + 3^{3n + 1} for all n is divisible by

3

11

2

4

Question 3 of 15

4. The sum of cubes of three consecutive natural numbers is divisible by:

2

9

7

5

Question 4 of 15

5. A.   B.   C.   D.   

A

B

C

D

Question 5 of 15

6. The smallest positive integer n, for which

2

3

4

1

Question 6 of 15

7. To prove a formula by principle of mathematical induction, we verify the statement

For as many positive integral values of n as we like

only for n = k, where k is any positive integer.

Once the formula is proved for a particular positive integer the formula will automatically follow for the next positive integer and the next indefinitely.

only for n = 1

Question 7 of 15

8. 2ⁿ  >  n² when n ∈ N such that

n > 2

n < 5

n > 3

n ≥ 5

Question 8 of 15

9. The greatest natural number, which divides (n + 1) (n +2) (n + 3)(n + 4) is

4

6

24

1

Question 9 of 15

10. If P(k) is the statement 2^3k - 1 is divisible by 7, then P(k + 1) is

2^{3k - 2} is divisible by 7

2^{3k + 2} - 1 is divisible by 7

2^{3k + 3} - 1 is divisible by 7

2^{3k + 1} - 1 is divisible by 7

Question 10 of 15

11. For each n ∈ N,  n(n + 1) (2n + 1) is divisible by:

5

7

6

11

Question 11 of 15

12. Let P(n) is the statement the product of two consecutive natural numbers is even. Then which of the following is true?

P(100)

P(n), n ∈ N

P(20)

P(3)

Question 12 of 15

13. For positive integers n, (1 + x)ⁿ > 1 + nx ; (x > - 1) when

n > 2

n ≥ 2

n ≥ 1

n ≤ 2

Question 13 of 15

14. Let P(n): 2ⁿ < 4n, then which of the following is true?

P(8)

P(4)

P(6)

P(3)

Question 14 of 15

15. The principle of mathematical induction is for the set of:

Rational numbers

Positive integers

Whole number

Integers

Question 15 of 15

 Loading...